Wave functions and half-off-shell $t$ matrix of a two-particle system

An integral representation that determines directly the partial wave functions and the half-off-shell t matrix of a two-particle system from scattering data is obtained. The representation has an explicitly controlled functional arbitrariness. If this is fixed in a manner equivalent to imposing the condition of locality on the interaction, the method developed is equivalent to the inverse scattering method. Other ways of fixing the arbitrariness correspond to different choices of nonlocal phase-equivalent potentials.